Which episode of each series do you think captures it the most?

It's hard to narrow it down to one episode.

TOS: One of the parallel Earth or computer must be reasoned to death episodes. "Bread and Circuses" or "Return of The Archons".

TNG: One of the bottle shows where the crew must solve a mystery that involves the computer or a character who is not what he appears. "Contagion" or "Clues" or "A Matter of Time" or "Conundrum".

DS9: One of the episodes that features a serious, high stakes A story involving the Bajorans, Cardassians, or The Dominion, and a lightheated B story that has absolutely nothing to do with the A story but is highly entertaining nonetheless. "Treachery, Faith, and The Great River".